My deepest sympathies for what you are going through.

You should certainly tell your advisor. No reasonable person would believe that you are using this situation as an "excuse" for poor performance.

Understanding your situation will help your advisor do his/her job: advising you according to your current needs and circumstances.

Your advisor may be able to direct you to mental health and other support services at your university that can help you through this time. He/she can also make you aware of other options that are available under exceptional circumstances: for example, a short leave of absence if you feel it is necessary, or an option to delay a comprehensive exam, or other similar concessions that can take some of the academic pressure off you while you focus on regaining your mental and emotional health.

My mother died shortly after I matriculated to my PhD program.

I actually could not finish all of my classes, and had to make up work the following semester.

Everyone involved (dept. head, advisor, etc.) would have given me even more time than I took to get back on track, after a few months I dove into work as a way to deal with some of parts of the loss.

Any reasonable university and advisor will give you time, most large universities even have formal bereavement policies for graduate students (in the US at least).

You should certainly tell your dean/dept. head about it as well as your advisor, and even take a leave of absence if you need to.

Don't be afraid to take some time, the work can wait.

A student in our program took a year's leave to look after his mother while she died of cancer. I am sure that anyone who thought of it, thought more of him not less of him for it.

You should always give your advisor all relevant information regarding your performance. He/she has to assess your progress and will inevitably have a view regarding whether you are bright, stupid, lazy, hardworking, distractable, etc. Unless you truly think they are an ogre give them the full picture.

It's completely understandable that you're struggling with your PhD program right now, given the challenging situation with your mom. Considering your academic performance has been good in the past, it's essential to be honest with your advisor about your current situation. Your advisor is there to support you, not just as a supervisor but also as a mentor. They can offer guidance, accommodations, or even temporary adjustments to your research goals and timeline. By sharing your struggles, you may be able to find ways to cope with your mental and emotional state, which in turn can help you regain focus and make progress on your research. It's unlikely that your advisor will view your situation as an excuse. In fact, many advisors have dealt with similar situations and can provide valuable advice and support. Your honesty will also show that you're proactive and committed to your research, even in difficult circumstances. Before speaking with your advisor, consider preparing a clear and concise explanation of your situation, including your mom's prognosis and how it's affecting your research. This will help you articulate your needs and potential solutions. Your advisor may be able to offer temporary extensions, changes in research focus, or even recommend resources to help you cope with your situation. Remember, your well-being and academic success are interconnected. By being open with your advisor, you can work together to find ways to manage your challenges and continue making progress on your PhD.